带非光滑核的多线性奇异积分算子的有界性

数学物理学报 ›› 2010, Vol. 30 ›› Issue (1): 167-178.

带非光滑核的多线性奇异积分算子的有界性

刘岚喆

长沙理工大学数学系长沙 410077

收稿日期:2008-05-07 修回日期:2009-09-05 出版日期:2010-01-01 发布日期:2010-01-01
基金资助:
国家自然科学基金(G.10271071)资助.

Boundedness Properties for Multilinear Singular Integral Operators with Non-Smooth Kernels

LIU Lan-Zhe

College of Mathematics, Changsha University of Science and Technology, Changsha 410077

Received:2008-05-07 Revised:2009-09-05 Online:2010-01-01 Published:2010-01-01
Supported by:
国家自然科学基金(G.10271071)资助.

摘要/Abstract

摘要：

该文对带非光滑核的多线性奇异积分算子建立了sharp 函数估计, 作为应用, 得到了该多线性奇异积分算子的L^p(1<p<∞) 范数不等式.

关键词: 多线性算子, 奇异积分算子, Sharp 函数估计, BMO 空间

Abstract:

In this paper, we establish a sharp function estimate for some multilinear singular integral operators with non-smooth kernels. As an application, we obtain the L^p(1

Key words: Multilinear operator, Singular integral operator, Sharp estimate, BMO

中图分类号:

42B20

刘岚喆. 带非光滑核的多线性奇异积分算子的有界性[J]. 数学物理学报, 2010, 30(1): 167-178.

LIU Lan-Zhe. Boundedness Properties for Multilinear Singular Integral Operators with Non-Smooth Kernels[J]. Acta mathematica scientia,Series A, 2010, 30(1): 167-178.

参考文献

[1] Chanillo S. A note on commutators. Indiana Univ Math J, 1982, 31: 7--16

[2] Cohen J. A sharp estimate for a multilinear singular integral on Rⁿ. Indiana Univ Math J, 1981, 30: 693--702

[3] Cohen J, Gosselin J. On multilinear singular integral operators on Rⁿ. Studia Math, 1982, 72: 199--223

[4] Cohen J, Gosselin J. A BMO estimate for multilinear singular integral operators. Illinois J Math, 1986, 30: 445--465

[5] Coifman R, Meyer Y. Wavelets, Calder\'on-Zygmund and Multilinear Operators. Cambridge Studies in Advanced Math 48. Cambridge: Cambridge University Press, 1997

[6] Deng D G, Yan L X. Commutators of singular integral operators with non-smooth kernels. Acta Math Scientia, 2005, 25(1): 137--144

[7] Ding Y, Lu S Z. Weighted boundedness for a class rough multilinear operators. Acta Math Sinica, 2001, 17: 517--526

[8] Duong X T, McIntosh A. Singular integral operators with non-smooth kernels on irregular domains. Rev Mat Iberoamericana, 1999, 15: 233--265

[9] Garcia-Cuerva J, Rubio de Francia J L. Weighted Norm Inequalities and Related Topics. Amsterdam: North-Holland, 1985

[10] Hu G, Yang D C. A variant sharp estimate for multilinear singular integral operators. Studia Math, 2000, 141: 25--42

[11] Martell J M. Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications.
Studia Math, 2004, 161: 113--145

[12] Pèrez C. Endpoint estimate for commutators of singular integral operators. J Func Anal, 1995, 128: 163--185

[13] Pèrez C, Pradolini G. Sharp weighted endpoint estimates for commutators of singular integral operators. Michigan Math J, 2001, 49: 23--37

[14] Pèrez C, Trujillo-Gonzalez R. Sharp weighted estimates for multilinear commutators. J London Math Soc, 2002, 65: 672--692

[15] Pèrez C, Trujillo-Gonzalez R. Sharp weighted estimates for vector-valued singular integral operators and commutators. Tohoku Math J, 2003, 55: 09--129

[16] Stein E M. Harmonic Analysis: Real Variable Methods, Orthogonality and Oscillatory Integrals. Princeton NJ: Princeton Univ Press, 1993